Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x+9y &= -6 \\ 8x+3y &= 2\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $3y = -8x+2$ Divide both sides by $3$ to isolate $y$ $y = {-\dfrac{8}{3}x + \dfrac{2}{3}}$ Substitute this expression for $y$ in the first equation. $6x+9({-\dfrac{8}{3}x + \dfrac{2}{3}}) = -6$ $6x - 24x + 6 = -6$ Simplify by combining terms, then solve for $x$ $-18x + 6 = -6$ $-18x = -12$ $x = \dfrac{2}{3}$ Substitute $\dfrac{2}{3}$ for $x$ back into the top equation. $6( \dfrac{2}{3})+9y = -6$ $4+9y = -6$ $9y = -10$ $y = -\dfrac{10}{9}$ The solution is $\enspace x = \dfrac{2}{3}, \enspace y = -\dfrac{10}{9}$.